# Function Differentiation Task

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A Function Differentiation Task is a mathematical task that requires the derivative of a function.

**AKA:**Derivative Function Identification.**Context:****Input:**Differentiable Function.- It can range from being a Manual Function Differentiation Task to being an Automated Function Differentiation Task.
- It can be solved by a Function Differentiation System.
- …

**See:**Gradient Function.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/derivative Retrieved:2015-1-11.
- The
**derivative**of a function of a real variable measures the sensitivity to change of a quantity (a function or dependent variable) which is determined by another quantity (the independent variable). It is a fundamental tool of calculus. …… The process of finding a derivative is called differentiation. The reverse process is called

*antidifferentiation*. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation and integration constitute the two fundamental operations in single-variable calculus.

- The

### 2009

- http://www.euclideanspace.com/maths/differential/vectorcalculus/index.htm
- Differentiation with respect to a scalar is defined as follows, if:
- f(x) = [a, b, c, Daniel S. Weld.

- then:
- d f(x) / dx = [d(a /dx), d(b/dx), d(c/dx), d(e/dx)]

- In other words to differentiate with respect to a scalar, we just differentiate the elements individually. So to give a more specific example if:
- f(x) = [xn, sin(x), tan(x), ex]

- then:
- d f(x) / dx = [n*xn-1, cos(x), sec2(x), ex]

- So this is quite simple, provided that we can differentiate the elements of a vector, we can differentiate the whole quaternion.

- Differentiation with respect to a scalar is defined as follows, if: